Predictive simulation of single-leg landing scenarios for ACL injury risk factors evaluation

The Anterior Cruciate Ligament (ACL) rupture is a very common knee injury during sport activities. Landing after jump is one of the most prominent human body movements that can lead to such an injury. The landing-related ACL injury risk factors have been in the spotlight of research interest. Over the years, researchers and clinicians acquire knowledge about human movement during daily-life activities by organizing complex in vivo studies that feature high complexity, costs and technical and most importantly physical challenges. In an attempt to overcome these limitations, this paper introduces a computational modeling and simulation pipeline that aims to predict and identify key parameters of interest that are related to ACL injury during single-leg landings. We examined the following conditions: a) landing height, b) hip internal and external rotation, c) lumbar forward and backward leaning, d) lumbar medial and lateral bending, e) muscle forces permutations and f) effort goal weight. Identified on related research studies, we evaluated the following risk factors: vertical Ground Reaction Force (vGRF), knee joint Anterior force (AF), Medial force (MF), Compressive force (CF), Abduction moment (AbdM), Internal rotation moment (IRM), quadricep and hamstring muscle forces and Quadriceps/Hamstrings force ratio (Q/H force ratio). Our study clearly demonstrated that ACL injury is a rather complicated mechanism with many associated risk factors which are evidently correlated. Nevertheless, the results were mostly in agreement with other research studies regarding the ACL risk factors. The presented pipeline showcased promising potential of predictive simulations to evaluate different aspects of complicated phenomena, such as the ACL injury.


FOOT-GROUND CONTACT
In this section we present selected parameters of the foot-ground contact model used for the simulations. The values were assigned based on other research studies [1] and are presented in S1

IMPLEMENTATION
The source code along with any related material for this publication are publicly available, providing scripts so that the readers can comprehend, reuse and reproduce the results of all the examined cases. Also, the resulted motion files and exported plots are all included. The following open source frameworks were used for the simulations: OpenSim, SCONE and Moco tool. All scripts are implemented using python. The experiments were conducted using a computer machine with an i7-9700 Intel(R) Core(TM) processor @3.00 GHz, a memory of 16GB, and a Windows 10 64bit operating system. Every simulation scenario required about 45 to 60 minutes to complete regarding the above specifications (except for the muscle force case study which required about 60 to 120 minutes per study).

A. Predict motion with SCONE
In this subsection, we present a general overview of the simulation setup and its basic components for predicting a single-leg landing motion in SCONE (in lua script).  As it can be noted, the Optimizer contains the musculoskeletal model at its initial state, a reflex controller and a composite measure. The reflex controller includes "MuscleReflex" entries that simulate proprioceptic reflexes and a "BodyPointReflex" that simulate the vestibular reflexes.
The composite measure contains the following measures: • A parameter that checks if the model falls below a specified value Penalties are applied when these measures are violated.

B. Simulations with Moco
Operations on the selected musculoskeletal models are valid for all the simulations in Moco (tracking and predictive) and are presented along with simulation setup steps in Moco.

B.1. Model operations
For all the simulations conducted in Moco (tracking and predictive), certain modifications were applied to the musculoskeletal model. The muscle model was selected as the "DeGrooteFregly" muscle type, since this model is compliant with Moco. The passive fiber forces were ignored and the active fiber force width for all muscles was scaled with a factor of 1.5. Ideal torque actuators were appended to the Degrees of Freedom (DoFs) that were not actuated by muscles. Also, reserve actuators were added to all DoFs to act supplementary to the already present muscles. The maximum torque was set to 100 Nm. All these operations are demonstrated next:

C. Track with Moco
Regarding the two tracking studies in Moco, the pipeline was similar, except from the musculoskeletal models. The simulation initial and final time were identical to these of the SCONE trajectory. The track tool instance was connected to the problem. Instantly the "MocoStateTrack-ingGoal" was added to the tracking study. Some states of the model were edited to further assist the trajectory solution. The bounds for these DoFs were set based on the initial and final states of the predicted motion from SCONE simulation. A detailed overview of these bounds is presented in S2 Table. For the DoFs that are not included in this table no bounds were set. Moreover, we applied bounds for the initial state and the entire motion for the activation of all muscles. At the first time instant the activation of all muscles was set to zero. Furthermore, both models consists of identical DoFs and the following description concerns both of them. An overview of the commands that were used to setup the analysis is presented next:

D. Predict motion with Moco
Regarding prediction in Moco, we created a new study for each investigated scenario. The main simulation setup which is valid for all the studies is presented in this subsection. Specific settings for each case study will be presented in the following sections. The common setting for all cases was the initial guess which was set as the MocoTrack output.

D.1. Initial height case study
In this section, we describe the simulation setup of drop-landing from different initial heights. The model used was "Gait2392". The pelvis joint vertical position value was modified in order to achieve landings from 30, 35, 40, 45, 50 and 55 cm of height. For every height value a new study was created with the parameters described previously. The solution acquired with the track tool was used as an initial guess for the solver. Also, the "MocoControlGoal" or effort goal was added to the problem with a weight of 0.001.
Apart from the pelvis joint vertical position value which was adjusted in order to achieve multiple initial landing heights, all the other DoFs remained identical for the initial state in all scenarios. It should be mentioned that a deviation of 0.01 cm of the selected landing height was allowed in all cases, as with all DoFs of the model.

D.2. Hip rotation case study
Again, we used the "Gait2392" OpenSim model, and the previously tracked solution was used as an initial guess for the solver. Also, the "MocoControlGoal" was added to the problem with a weight of 0.001. In S3 Table we display the bounds assigned to all DoFs in the Moco studies. For hip_adduction of the left lower limb we did not assign bounds because it is highly related to hip_rotation and we wanted to examine how it will respond to different conditions of hip rotation.

DoFs
Initial bounds Final bounds Bounds  Regarding the trunk orientation case study, different studies were produced using the initial guess described previously and certain bounds for the initial and final states that are presented in S5 Table, S4 Table. The musculoskeletal model was "Gait2392" and the "MocoControlGoal" or effort goal was added to the problem with a weight of 0.002.

D.4. Muscle force of knee joint agonists and antagonists case study
For the muscle forces case study, the model used was "Gait2392" and the effort goal was added to the problem with a weight of 0. The quadriceps muscles include rectus femoris, vastus medialis, vastus lateralis and vastus intermedialis. Hamstrings muscle group combines the semimembranosus, semitendinosous, biceps femoris long head and biceps femoris short head. In S6 Table we display the value of the standard max isometric force fore each muscle, along with the value when it is weakened or strengthened. Based on S6 Table, nine cases were simulated with different combinations of normal, weak and strong muscles. These cases are demonstrated in S7 Table.